Frontbencher Steve Ciobo said it was a decision for Mrs Bishop to make in the best interests of herself and her constituents.

"That's a decision for Bronwyn," he told Sky. "I think it's important to separate her role as Speaker from her role as the federal member for Mackellar. They are two jobs...they are separate processes."

The Prime Minister agreed the scandal would cost the government, including himself.

"There is a price to pay. Sure the government has inevitably paid a price and I daresay there will be a little personal price for me," he said.

There is a hot race under way for who will replace Mrs Bishop as Speaker, with Mrs Bishop's veteran colleague Phillip Ruddock and South Australian Andrew Southcott both declaring their intention to contest the position.

Victorian Liberal MP Tony Smith is also considered a possible candidate. He did not return calls on Tuesday. Brisbane MP Teresa Gambaro is also being named, but it is considered highly unlikely she would nominate.

Mr Abbott, who is in Adelaide to make a major announcement on new naval ships to be built there, said he discussed the speakership issue with Dr Southcott last night.

Writing in his column for News Corp, Mr Reith's one-time cabinet colleague, former treasurer Peter Costello, took aim at the "woodchucks ... desperate for advancement", who engage in a faux competition of displaying "uber loyalty" towards the Prime Minister.

"These people are now busily burying the transcripts where they predicted the whole thing was just a storm in a teacup. They are useful in carrying a line but no help in making a decision," Mr Costello wrote.

"A leader's best advisers are the ones prepared to tell him what he doesn't want to hear."

While Mr Costello did not name names, Assistant Treasurer Josh Frydenberg, who is widely considered to be a rising star in the government, was one notable defender of the former Speaker.

Mr Frydenberg dismissed the furore surrounding Mrs Bishop's decision to claim travel entitlements to attend the weddings of Liberal friends as "the politics of distraction".

"She said there was official business and I take Bronwyn at her word on that. I don't think the punishment would fit the crime if she were to resign," he told Sky News.

"I think this is the politics of distraction."

Cabinet minister Christopher Pyne, who serves as the government's leader in the House, has also strongly defended Mrs Bishop, including praising her as an "excellent Speaker" following her resignation on Sunday.

"Labor will do anything to distract people from Bill Shorten's failure as leader…this is all a massive distraction," Mr Pyne told the Nine Network's Today show last Friday.